A particle is moving with the given data. Find the position of the particle.?

Question

v(t) = 1.5sqrt(t), s(4) = 10

Answer 1

If you integrate v(t) = 1.5sqrt(t) you get s(t) = t^1.5 + c. Putting in s(4) = 10 gives 10 = 4^1.5 + c which is 10 = 8 + c so c = 2. Therefore s = 2 + t^1.5

Answer 2

v(t) = ds/dt So s is the integral of v(t)
ds= 1.5 t^1/2 dt so s= 1.5*2/3*t^3/2 +C
s=t^3/2+C you'll find the value of C as you know s(4)=10

s(4)= 4^3/2 +C=10 8+C=10 so C=2

s= t^3/2+2